A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
The Extended Centralizer of a Ring Over a Module

1951
*
Proceedings of the American Mathematical Society
*

In a recent paper,1 K. Asano gave a new proof of the theorem that a domain of integrity has a right quotient ring if and only if every pair of nonzero elements has a common nonzero right multiple. His method of proof is used in the present work to extend the centralizer of a ring over a module to a system of semi-endomorphisms of the module. From this extension, necessary and sufficient conditions that a ring have a right quotient regular ring are derived. Consider a given ring R, and a given

doi:10.2307/2031703
fatcat:2me5apx3bzaujbi6iwvrbtbgpe